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@ -1,17 +1,17 @@
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mapgen_rivers
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=============
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Procedural map generator for Minetest 5.x. Still experimental and basic.
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Procedural map generator for Minetest 5.x. Focused on river networks, and features valley erosion and lakes.
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Contains two distinct programs: Python scripts for pre-processing, and Lua scripts to generate the map on Minetest.
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# Installation
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This mod should be placed in the `/mods` directory like any other Minetest mod.
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The Python part relies on external libraries that you need to install:
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- `numpy`, a widely used library for numerical calculations
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- `numpy` and `scipy`, widely used libraries for numerical calculations
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- `noise`, doing Perlin/Simplex noises
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- optionally, `matplotlib` (for map preview)
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@ -23,7 +23,7 @@ Run the script `terrain_rivers.py` via command line. You can optionally append t
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```
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./terrain_rivers.py 1000
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```
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For a default 400x400 map, it should take between 1 and 2 minutes. It will generate 5 files directly in the mod folder, containing the map data (1.4 MB for the default size).
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For a default 401x401 map, it should take between 1 and 2 minutes. It will generate 5 files directly in the mod folder, containing the map data.
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## Map generation
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Just create a Minetest world with `singlenode` mapgen, enable this mod and start the world. The data files are immediately copied in the world folder so you can re-generate them afterwards, it won't affect the old worlds.
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16
bounds.py
16
bounds.py
@ -1,7 +1,10 @@
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import numpy as np
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import matplotlib.pyplot as plt
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def make_bounds(dirs, rivers):
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"""
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Give an array of all horizontal and vertical bounds
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"""
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(Y, X) = dirs.shape
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bounds_h = np.zeros((Y, X-1), dtype='i4')
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bounds_v = np.zeros((Y-1, X), dtype='i4')
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@ -14,6 +17,10 @@ def make_bounds(dirs, rivers):
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return bounds_h, bounds_v
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def get_fixed(dirs):
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"""
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Give the list of points that should not be twisted
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"""
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borders = np.zeros(dirs.shape, dtype='?')
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borders[-1,:] |= dirs[-1,:]==1
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borders[:,-1] |= dirs[:,-1]==2
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@ -28,6 +35,11 @@ def get_fixed(dirs):
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return borders | ~donors
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def twist(bounds_x, bounds_y, fixed, d=0.1, n=5):
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"""
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Twist the grid (define an offset for every node). Model river bounds as if they were elastics.
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Smoothes preferentially big rivers.
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"""
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moveable = ~fixed
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(Y, X) = fixed.shape
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@ -55,7 +67,7 @@ def twist(bounds_x, bounds_y, fixed, d=0.1, n=5):
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length = np.hypot(force_x, force_y)
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length[length==0] = 1
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coeff = d / length * moveable
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coeff = d / length * moveable # Normalize, take into account the direction only
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offset_x += force_x * coeff
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offset_y += force_y * coeff
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27
erosion.py
27
erosion.py
@ -3,22 +3,33 @@ import scipy.ndimage as im
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import rivermapper as rm
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def advection(dem, dirs, rivers, time, K=1, m=0.5, sea_level=0):
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"""
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Simulate erosion by rivers.
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This models erosion as an upstream advection of elevations ("erosion waves").
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Advection speed depends on water flux and parameters:
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v = K * flux^m
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"""
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dirs = dirs.copy()
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dirs[0,:] = 0
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dirs[-1,:] = 0
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dirs[:,0] = 0
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dirs[:,-1] = 0
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adv_time = 1 / (K*rivers**m)
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adv_time = 1 / (K*rivers**m) # For every pixel, calculate the time an "erosion wave" will need to cross it.
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dem = np.maximum(dem, sea_level)
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dem_new = np.zeros(dem.shape)
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for y in range(dirs.shape[0]):
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for x in range(dirs.shape[1]):
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# Elevations propagate upstream, so for every pixel we seek the downstream pixel whose erosion wave just reached the current pixel.
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# This means summing the advection times downstream until we reach the erosion time.
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x0, y0 = x, y
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x1, y1 = x, y
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remaining = time
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while True:
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# Move one pixel downstream
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flow_dir = dirs[y0,x0]
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if flow_dir == 0:
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remaining = 0
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@ -32,19 +43,19 @@ def advection(dem, dirs, rivers, time, K=1, m=0.5, sea_level=0):
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elif flow_dir == 4:
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x1 -= 1
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if remaining <= adv_time[y0,x0]:
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if remaining <= adv_time[y0,x0]: # Time is over, we found it.
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break
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remaining -= adv_time[y0,x0]
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x0, y0 = x1, y1
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c = remaining / adv_time[y0,x0]
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dem_new[y,x] = c*dem[y1,x1] + (1-c)*dem[y0,x0]
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dem_new[y,x] = c*dem[y1,x1] + (1-c)*dem[y0,x0] # If between 2 pixels, perform linear interpolation.
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return np.minimum(dem, dem_new)
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def diffusion(dem, time, d=1):
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radius = d * time**.5
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return im.gaussian_filter(dem, radius, mode='reflect')
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return im.gaussian_filter(dem, radius, mode='reflect') # Diffusive erosion is a simple Gaussian blur
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class EvolutionModel:
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def __init__(self, dem, K=1, m=0.5, d=1, sea_level=0, flow=False, flex_radius=100):
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@ -78,9 +89,9 @@ class EvolutionModel:
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self.flow_uptodate = False
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def define_isostasy(self):
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self.ref_isostasy = im.gaussian_filter(self.dem, self.flex_radius, mode='reflect')
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self.ref_isostasy = im.gaussian_filter(self.dem, self.flex_radius, mode='reflect') # Define a blurred version of the DEM that will be considered as the reference isostatic elevation.
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def adjust_isostasy(self, rate=1):
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isostasy = im.gaussian_filter(self.dem, self.flex_radius, mode='reflect')
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correction = (self.ref_isostasy - isostasy) * rate
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self.dem = self.dem + correction
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isostasy = im.gaussian_filter(self.dem, self.flex_radius, mode='reflect') # Calculate blurred DEM
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correction = (self.ref_isostasy - isostasy) * rate # Compare it with the reference isostasy
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self.dem = self.dem + correction # Adjust
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10
geometry.lua
10
geometry.lua
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local function distance_to_segment(x1, y1, x2, y2, x, y)
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-- get the distance between point (x,y) and segment (x1,y1)-(x2,y2)
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local a = (x1-x2)^2 + (y1-y2)^2
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local a = (x1-x2)^2 + (y1-y2)^2 -- square of distance
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local b = (x1-x)^2 + (y1-y)^2
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local c = (x2-x)^2 + (y2-y)^2
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if a + b < c then
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-- The closest point of the segment is the extremity 1
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return math.sqrt(b)
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elseif a + c < b then
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-- The closest point of the segment is the extremity 2
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return math.sqrt(c)
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else
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-- The closest point is on the segment
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return math.abs(x1 * (y2-y) + x2 * (y-y1) + x * (y1-y2)) / math.sqrt(a)
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end
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end
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local function transform_quadri(X, Y, x, y)
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-- X, Y 4-vectors giving the coordinates of the 4 nodes
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-- To index points in an irregular quadrilateral, giving x and y between 0 (one edge) and 1 (opposite edge)
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-- X, Y 4-vectors giving the coordinates of the 4 vertices
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-- x, y position to index.
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local x1, x2, x3, x4 = unpack(X)
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local y1, y2, y3, y4 = unpack(Y)
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-- Compare distance to 2 opposite edges, they give the X coordinate
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local d23 = distance_to_segment(x2,y2,x3,y3,x,y)
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local d41 = distance_to_segment(x4,y4,x1,y1,x,y)
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local xc = d41 / (d23+d41)
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-- Same for the 2 other edges, they give the Y coordinate
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local d12 = distance_to_segment(x1,y1,x2,y2,x,y)
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local d34 = distance_to_segment(x3,y3,x4,y4,x,y)
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local yc = d12 / (d12+d34)
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6
init.lua
6
init.lua
@ -12,6 +12,7 @@ local make_polygons = dofile(modpath .. 'polygons.lua')
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local transform_quadri = dofile(modpath .. 'geometry.lua')
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-- Linear interpolation
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local function interp(v00, v01, v11, v10, xf, zf)
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local v0 = v01*xf + v00*(1-xf)
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local v1 = v11*xf + v10*(1-xf)
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@ -44,6 +45,7 @@ local function generate(minp, maxp, seed)
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local xf, zf = transform_quadri(poly.x, poly.z, x/blocksize, z/blocksize)
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local i00, i01, i11, i10 = unpack(poly.i)
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-- Test the 4 edges to see whether we are in a river or not
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local is_river = false
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local depth_factor = 0
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local r_west, r_north, r_east, r_south = unpack(poly.rivers)
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@ -66,7 +68,7 @@ local function generate(minp, maxp, seed)
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zf = 0
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end
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if not is_river then
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if not is_river then -- Test corners also
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local c_NW, c_NE, c_SE, c_SW = unpack(poly.river_corners)
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if xf+zf < c_NW then
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is_river = true
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@ -87,7 +89,7 @@ local function generate(minp, maxp, seed)
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end
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end
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if not is_river then
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if not is_river then -- Redefine indicesto have 0/1 on the riverbanks (avoids ugly edge cuts, at least for small rivers)
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xf = (xf-r_west) / (r_east-r_west)
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zf = (zf-r_north) / (r_south-r_north)
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end
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22
polygons.lua
22
polygons.lua
@ -44,6 +44,7 @@ for k, v in ipairs(offset_z) do
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offset_z[k] = (v+0.5)/256
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end
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-- To index a flat array representing a 2D map
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local function index(x, z)
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return z*X+x+1
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end
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@ -66,26 +67,33 @@ local function river_width(flow)
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return math.min(wfactor * flow ^ wpower, 1)
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end
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-- On map generation, determine into which polygon every point (in 2D) will fall.
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-- Also store polygon-specific data
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local function make_polygons(minp, maxp)
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local chulens = maxp.z - minp.z + 1
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local polygons = {}
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-- Determine the minimum and maximum coordinates of the polygons that could be on the chunk, knowing that they have an average size of 'blocksize' and a maximal offset of 0.5 blocksize.
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local xpmin, xpmax = math.max(math.floor(minp.x/blocksize - 0.5), 0), math.min(math.ceil(maxp.x/blocksize), X-2)
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local zpmin, zpmax = math.max(math.floor(minp.z/blocksize - 0.5), 0), math.min(math.ceil(maxp.z/blocksize), Z-2)
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-- Iterate over the polygons
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for xp = xpmin, xpmax do
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for zp=zpmin, zpmax do
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local iA = index(xp, zp)
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local iB = index(xp+1, zp)
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local iC = index(xp+1, zp+1)
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local iD = index(xp, zp+1)
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-- Extract the vertices of the polygon
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local poly_x = {offset_x[iA]+xp, offset_x[iB]+xp+1, offset_x[iC]+xp+1, offset_x[iD]+xp}
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local poly_z = {offset_z[iA]+zp, offset_z[iB]+zp, offset_z[iC]+zp+1, offset_z[iD]+zp+1}
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local polygon = {x=poly_x, z=poly_z, i={iA, iB, iC, iD}}
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local bounds = {}
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local bounds = {} -- Will be a list of the intercepts of polygon edges for every X position (scanline algorithm)
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-- Calculate the min and max X positions
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local xmin = math.max(math.floor(blocksize*math.min(unpack(poly_x)))+1, minp.x)
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local xmax = math.min(math.floor(blocksize*math.max(unpack(poly_x))), maxp.x)
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-- And initialize the arrays
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for x=xmin, xmax do
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bounds[x] = {}
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end
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@ -93,27 +101,33 @@ local function make_polygons(minp, maxp)
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local i1 = 4
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for i2=1, 4 do -- Loop on 4 edges
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local x1, x2 = poly_x[i1], poly_x[i2]
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-- Calculate the integer X positions over which this edge spans
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local lxmin = math.floor(blocksize*math.min(x1, x2))+1
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local lxmax = math.floor(blocksize*math.max(x1, x2))
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if lxmin <= lxmax then
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if lxmin <= lxmax then -- If there is at least one position in it
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local z1, z2 = poly_z[i1], poly_z[i2]
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-- Calculate coefficient of the equation defining the edge: Z=aX+b
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local a = (z1-z2) / (x1-x2)
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local b = blocksize*(z1 - a*x1)
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for x=math.max(lxmin, minp.x), math.min(lxmax, maxp.x) do
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-- For every X position involved, add the intercepted Z position in the table
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table.insert(bounds[x], a*x+b)
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end
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end
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i1 = i2
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end
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for x=xmin, xmax do
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-- Now sort the bounds list
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local xlist = bounds[x]
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table.sort(xlist)
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local c = math.floor(#xlist/2)
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for l=1, c do
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-- Take pairs of Z coordinates: all positions between them belong to the polygon.
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local zmin = math.max(math.floor(xlist[l*2-1])+1, minp.z)
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local zmax = math.min(math.floor(xlist[l*2]), maxp.z)
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local i = (x-minp.x) * chulens + (zmin-minp.z) + 1
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for z=zmin, zmax do
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-- Fill the map at these places
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polygons[i] = polygon
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i = i + 1
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end
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@ -123,10 +137,13 @@ local function make_polygons(minp, maxp)
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polygon.dem = {dem[iA], dem[iB], dem[iC], dem[iD]}
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polygon.lake = math.min(lakes[iA], lakes[iB], lakes[iC], lakes[iD])
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-- Now, rivers.
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-- Start by finding the river width (if any) for the polygon's 4 edges.
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local river_west = river_width(bounds_z[iA])
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local river_north = river_width(bounds_x[iA-zp])
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local river_east = 1-river_width(bounds_z[iB])
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local river_south = 1-river_width(bounds_x[iD-zp-1])
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-- Only if opposite rivers overlap (should be rare)
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if river_west > river_east then
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local mean = (river_west + river_east) / 2
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river_west = mean
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@ -139,6 +156,7 @@ local function make_polygons(minp, maxp)
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end
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polygon.rivers = {river_west, river_north, river_east, river_south}
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-- Look for river corners
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local around = {0,0,0,0,0,0,0,0}
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if zp > 0 then
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around[1] = river_width(bounds_z[iA-X])
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@ -19,9 +19,14 @@ neighbours_dirs = np.array([
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neighbours_pattern = neighbours_dirs > 0
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def flow_dirs_lakes(dem, random=0):
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"""
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Calculates flow direction in D4 (4 choices) for every pixel of the DEM
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Also returns an array of lake elevation
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"""
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(Y, X) = dem.shape
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dem_margin = np.zeros((Y+2, X+2))
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dem_margin = np.zeros((Y+2, X+2)) # We need a margin of one pixel at every edge, to prevent crashes when scanning the neighbour pixels on the borders
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dem_margin[1:-1,1:-1] = dem
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if random > 0:
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dem_margin += np.random.random(dem_margin.shape) * random
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@ -41,10 +46,11 @@ def flow_dirs_lakes(dem, random=0):
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dem_east = dem_margin[y,X]
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borders.append((dem_east, dem_east, y, X))
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# Make a binary heap
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heapq.heapify(borders)
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dirs = np.zeros((Y+2, X+2), dtype='u1')
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dirs[-2:,:] = 1
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dirs[-2:,:] = 1 # Border pixels flow outside the map
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dirs[:,-2:] = 2
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dirs[ :2,:] = 3
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dirs[:, :2] = 4
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@ -56,21 +62,26 @@ def flow_dirs_lakes(dem, random=0):
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heapq.heappush(borders, (alt, altmax, y, x))
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while len(borders) > 0:
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(alt, altmax, y, x) = heapq.heappop(borders)
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(alt, altmax, y, x) = heapq.heappop(borders) # Take the lowest pixel in the queue
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neighbours = dirs[y-1:y+2, x-1:x+2]
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empty_neighbours = (neighbours == 0) * neighbours_pattern
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neighbours += empty_neighbours * neighbours_dirs
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empty_neighbours = (neighbours == 0) * neighbours_pattern # Find the neighbours whose flow direction is not yet defined
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neighbours += empty_neighbours * neighbours_dirs # They flow into the pixel being studied
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lake = max(alt, altmax)
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lake = max(alt, altmax) # Set lake elevation to the maximal height of the downstream section.
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lakes[y-1,x-1] = lake
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coords = np.transpose(empty_neighbours.nonzero())
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for (dy,dx) in coords-1:
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for (dy,dx) in coords-1: # Add these neighbours into the queue
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add_point(y+dy, x+dx, lake)
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return dirs[1:-1,1:-1], lakes
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def accumulate(dirs, dem=None):
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"""
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Calculates the quantity of water that accumulates at every pixel,
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following flow directions.
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"""
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(Y, X) = dirs.shape
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dirs_margin = np.zeros((Y+2,X+2))-1
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dirs_margin[1:-1,1:-1] = dirs
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@ -79,13 +90,13 @@ def accumulate(dirs, dem=None):
|
||||
def calculate_quantity(y, x):
|
||||
if quantity[y,x] > 0:
|
||||
return quantity[y,x]
|
||||
q = 1
|
||||
q = 1 # Consider that every pixel contains a water quantity of 1 by default.
|
||||
neighbours = dirs_margin[y:y+3, x:x+3]
|
||||
donors = neighbours == neighbours_dirs
|
||||
donors = neighbours == neighbours_dirs # Identify neighbours that give their water to the pixel being studied
|
||||
|
||||
coords = np.transpose(donors.nonzero())
|
||||
for (dy,dx) in coords-1:
|
||||
q += calculate_quantity(y+dy, x+dx)
|
||||
q += calculate_quantity(y+dy, x+dx) # Add water quantity of the donors pixels (this triggers calculation for these pixels, recursively)
|
||||
quantity[y, x] = q
|
||||
return q
|
||||
|
||||
@ -96,5 +107,9 @@ def accumulate(dirs, dem=None):
|
||||
return quantity
|
||||
|
||||
def flow(dem):
|
||||
"""
|
||||
Calculates flow directions and water quantity
|
||||
"""
|
||||
|
||||
dirs, lakes = flow_dirs_lakes(dem)
|
||||
return dirs, lakes, accumulate(dirs, dem)
|
||||
|
||||
@ -20,28 +20,29 @@ else:
|
||||
scale = (mapsize-1) / 2
|
||||
n = np.zeros((mapsize, mapsize))
|
||||
|
||||
#micronoise_depth = 0.05
|
||||
|
||||
# Set noise parameters
|
||||
params = {
|
||||
"octaves" : int(np.ceil(np.log2(mapsize-1)))+1,
|
||||
"persistence" : 0.5,
|
||||
"lacunarity" : 2.,
|
||||
}
|
||||
|
||||
# Determine noise offset randomly
|
||||
xbase = np.random.randint(65536)
|
||||
ybase = np.random.randint(65536)
|
||||
|
||||
# Generate the noise
|
||||
for x in range(mapsize):
|
||||
for y in range(mapsize):
|
||||
n[x,y] = noise.snoise2(x/scale + xbase, y/scale + ybase, **params)
|
||||
|
||||
#micronoise = np.random.rand(mapsize, mapsize)
|
||||
#nn = np.exp(n*2) + micronoise*micronoise_depth
|
||||
nn = n*mapsize/5 + mapsize/20
|
||||
|
||||
# Initialize landscape evolution model
|
||||
print('Initializing model')
|
||||
model = EvolutionModel(nn, K=1, m=0.35, d=1, sea_level=0)
|
||||
|
||||
# Run the model's processes: the order in which the processes are run is arbitrary and could be changed.
|
||||
print('Flow calculation 1')
|
||||
model.calculate_flow()
|
||||
|
||||
@ -68,12 +69,15 @@ model.calculate_flow()
|
||||
|
||||
print('Done')
|
||||
|
||||
# Twist the grid
|
||||
bx, by = bounds.make_bounds(model.dirs, model.rivers)
|
||||
ox, oy = bounds.twist(bx, by, bounds.get_fixed(model.dirs))
|
||||
|
||||
# Convert offset in 8-bits
|
||||
offset_x = np.clip(np.floor(ox * 256), -128, 127)
|
||||
offset_y = np.clip(np.floor(oy * 256), -128, 127)
|
||||
|
||||
# Save the files
|
||||
save(model.dem, 'dem', dtype='>i2')
|
||||
save(model.lakes, 'lakes', dtype='>i2')
|
||||
save(np.abs(bx), 'bounds_x', dtype='>i4')
|
||||
@ -86,6 +90,7 @@ save(model.rivers, 'rivers', dtype='>u4')
|
||||
with open('size', 'w') as sfile:
|
||||
sfile.write('{:d}\n{:d}'.format(mapsize, mapsize))
|
||||
|
||||
# Display the map if matplotlib is found
|
||||
try:
|
||||
import matplotlib.pyplot as plt
|
||||
|
||||
@ -111,7 +116,7 @@ try:
|
||||
plt.pcolormesh(model.rivers, vmin=0, vmax=mapsize**2/25, cmap='Blues')
|
||||
plt.gca().set_aspect('equal', 'box')
|
||||
#plt.colorbar(orientation='horizontal')
|
||||
plt.title('Rivers discharge')
|
||||
plt.title('Rivers flux')
|
||||
|
||||
plt.show()
|
||||
except:
|
||||
|
||||
@ -34,6 +34,6 @@ plt.subplot(1,3,3)
|
||||
plt.pcolormesh(np.log(rivers), vmin=0, vmax=np.log(n/25), cmap='Blues')
|
||||
plt.gca().set_aspect('equal', 'box')
|
||||
#plt.colorbar(orientation='horizontal')
|
||||
plt.title('Rivers discharge')
|
||||
plt.title('Rivers flux')
|
||||
|
||||
plt.show()
|
||||
|
||||
Loading…
Reference in New Issue
Block a user